Geometry, Arithmetic, Architecture. Calculation Methods for Vault Surfaces in the Modo di Misurare le Fabriche by Guarini

The Modo di misurare le fabriche (1674), by Guarino Guarini is a treatise devoted to the explanation of methods to calculate surfaces and volumes. This treatise is one of the least studied among Guarini’s theoretical works. Referring to Euclides adauctus (1671), Guarini expresses the desire to make the geometric principles developed therein applicable and accessible, providing methods of measurement of works under construction in the second expansion of the Baroque city. The second part of the book, which is dedicated to the calculation of 3D surfaces, constantly refers to the intradosal surfaces of the vaults that constitute the prevailing cover of the coeval atria, main halls, and rooms. In the treatise, the elements that make up the vaulted systems (coves, groins, and domes) are reduced to the elementary geometries that shape them. The different sections, together with the combination of different shapes, offer examples on which Guarini proposes new exact or approximate calculation methods. Previously, the author carried out a reconstructive modeling on the XIX and XX plates of the Architettura civile, which allowed identifying a real vocabulary of shapes that can be used to generate multiple composed vaulted systems. Three-dimensional digital modeling, realized for the present research on Guarini graphic schemes, allows us: to verify the degree of accuracy of the proposed calculation methods, by comparing the analytical calculation of the surfaces applying Guarini’s formulas and the automatic calculation offered by the modeling software; and to compare and enrich (with new shapes) the casuistry present in the Architettura civile.